It is hard to come up with an electrical analogy.

Switch mode is like a single pole, "3 way switch", which normally has 3 terminals. Two terminals are the "travelers", the third terminal is the output.
Two 3 way switches are used to light a hallway, alternately from either end of the hallway.

Button mode is like the crush ice button on an appliance, which only runs the blade when held pressed in. But this
analogy lacks a function for the upper input, which is null. Some kind of logic gate might be better.

The clutch on a car is an example of button mode? Un-pushed for normal travel, pushed in for changing gears...

- Brian